Abstract

The properties of general involutional matrices satisfying the equationAm = kI, k = const, are studied. Generating equations for the induced representations of an arbitrary (n × n) matrix are explicitly written down. The special case when n = 3 is discussed in detail. It is shown that the conditions which make an arbitrary (n × n) matrix involutional leave any of its induced representation involutional. It is further shown that an involutional matrix in its self‐representation can be expanded in the basis of generalized Clifford algebra with coefficients which are the generalized hyperbolic functions. Eigenvalues of induced matrices, in particular when they are involutional, are calculated.